Rice Vector Library (”RVL”). A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms. The Rice Vector Library is a collection of C++ classes expressing core concepts (vector, function,…) of calculus in Hilbert space with minimal implementation dependence, and providing standardized interfaces behind which to hide application-dependent implementation details (data containers, function objects). A variety of coordinate-free algorithms from linear algebra and optimization, including Krylov subspace methods and various relatives of Newton’s method for nonlinear equations and constrained and unconstrained optimization, may be expressed purely in terms of this system of classes. The resulting code may be used without alteration in a wide range of control, design, and parameter estimation applications, in serial and parallel computing environments.